Problem: Rewrite as a simplified fraction. ${1.1\overline{8} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 118.8888...\\ 10x &= 11.8888...\end{align*}}$ Subtracting the two equations, we have: ${90x = 107}$ ${x = \dfrac{107}{90}} \text{or} {1 \dfrac{17}{90}}$